Question

4. If the lines given by 3x + 2ky = 2 and 2x + 5y +1 = 0 are parall
value of k is​

Answer 1

Answer:

15/4

Step-by-step explanation:

Given the pair of parallel lines.

The respective equations are :-

• 3x + 2ky - 2 = 0
• 2x + 5y + 1 = 0

Now, we know that,

If two parallel lines have the equations :-

• a1x + b1y + c1 = 0
• a2x + b2y + c2 = 0

Then, the conditon is :-

• a1/a2 = b1/b2 ≠ c1/c2

Therefore, we have,

=> 3/2 = 2k/5

=> 2k = (3 × 5)/2

=> 2k = 15/2

=> k = 15/(2×2)

=> k = 15/4

Hence, required value of k = 15/4.

Answer 2

If two parallel lines having equations ,

• $\bold{\bf{\red{a_1 x+b_1 y +c_1=0}}}$

• $\bold{\bf{\blue{a_{2} x+b_{2} y +c_2=0}}}$

Then the condition is ,

• $\bold{\bf{\red{\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq \frac{c_1}{c_2} }}}$

Now compare given two equations 3x+2ky-2=0 & 2x+5y+1=0 with above general equations,

$\implies \bold{a_1=3,b_1=2k,c_1=-2,a_2=2,b_2=5,c_2=1}$

Now according to the condition ,

$\implies \bold{\frac{3}{2}=\frac{2k}{5}\neq \frac{-2}{1} }$

$\implies \bold{\frac{3}{2}=\frac{2k}{5}}\\\\\implies \bold{\bf{\blue{k=\frac{15}{4} }}}$